Experimental Mathematics

Central binomial sums, multiple Clausen values, and zeta values

Jonathan Michael Borwein, David J. Broadhurst, and Joel Kamnitzer


We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Apery sums). The study of nonalternating sums leads to an investigation of different types of sums which we call multiple Clausen values. The study of alternating sums leads to a tower of experimental results involving polylogarithms in the golden ratio.

Article information

Experiment. Math., Volume 10, Issue 1 (2001), 25-34.

First available in Project Euclid: 30 August 2001

Permanent link to this document

Mathematical Reviews number (MathSciNet)
MR1 821 569

Zentralblatt MATH identifier

Primary: 11Mxx: Zeta and $L$-functions: analytic theory
Secondary: 05Axx: Enumerative combinatorics {For enumeration in graph theory, see 05C30} 11Bxx: Sequences and sets 33Bxx: Elementary classical functions

binomial sums multiple zeta values log-sine integrals Clausen's function multiple Clausen values polylogarithms Apéry sums


Borwein, Jonathan Michael; Broadhurst, David J.; Kamnitzer, Joel. Central binomial sums, multiple Clausen values, and zeta values. Experiment. Math. 10 (2001), no. 1, 25--34. https://projecteuclid.org/euclid.em/999188418

Export citation